APP MTH 7049 - Applied Mathematics Topic D
North Terrace Campus - Semester 2 - 2020
General Course Information
Course Code APP MTH 7049 Course Applied Mathematics Topic D Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y Course Description Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au
Course Coordinator: Professor Lewis Mitchell
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 2019, the topic of this course is Mathematical Biology and Physiology.
For centuries, mathematical models have been used in the physical sciences to help us understand problems such as the propagation of light, the motion of the planets, or the flow of fluids. More recently, mathematical models have been applied to problems in the life sciences, yielding important new insights into biological problems, and stimulating the development of new mathematics. This cross-fertilisation between the disciplines makes mathematical biology and physiology one of the most exciting (and challenging) areas of applied mathematics. In this course, we will study some important biological problems where mathematical models in the form of systems of ODEs and PDEs have produced new understanding. Unfortunately, most biologically interesting models cannot be solved analytically, and so we we need to develop expertise in alternative techniques for understanding their behaviour, including phase plane analysis, bifurcation theory and perturbation methods.
Topics covered will include:
-ion transport and propagation of signals in nerve cells (Hodgkin-Huxley equations)
-model development using conservation laws
-models for cell movement
-development of patterns in tissues (Keller-Segel model, Turing patterns)
Assumed knowledge for the course is a basic understanding of ODEs and PDEs, as covered in Modelling with ODEs III and Waves and PDES III.
On successful completion of this course, students will be able to:
1. develop ODE models for enzyme-catalysed reactions using the Law of Mass Action;
2. understand how Michaelis-Menten kinetics can be derived using perturbation theory;
3. understand and explain models for ion transport;
4. use phase-plane techniques to study the dynamics of ODE models such as the Hodgkin-Huxley equations;
5. understand conservation laws, and be able to use them to develop new models;
6. understand what is meant by a travelling wave solution, and be able to demonstrate their existence for Fisher's equation and other; systems;
7. understand the principles underpinning the Keller-Segel and Turing models for pattern formation, and use stability analysis to predict when it will occur in these and similar models;
8. recognise free boundary problems arising in tumour growth, and use some basic analytical techniques to study them.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
1,5 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
Recommended ResourcesL. Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics, 2005.
J. D. Murray, Mathematical Biology (two volumes), Springer, 2002.
Online LearningThe course will have an active MyUni website.
Learning & Teaching Activities
Learning & Teaching ModesThe lecturer guides the students through the course material in 30 lectures. Students are expected to engage with the material in the lectures. Interaction with the lecturer and discussion of any difficulties that arise during the lecture is encouraged. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 30 90 Assignments 4 66 Total 156
Learning Activities SummaryLecture outline
Enzyme catalysed reactions, the Law of Mass Action, Michaelis-Menten kinetics (4 Lectures).
Ion transport, excitable systems the Hodgkin-Huxley equations (5 Lectures).
Conservation laws, cell movement, reaction-advection diffusion equations, age-structured models (6 Lectures).
Fisher's equation, travelling waves (4 Lectures)
Pattern formation, Keller-Segel model, linear stability analysis, Turing patterns, diffusion-driven instability (6 lectures)
Domain growth, free boundary problems, avascular tumour models, development of the necrotic core (4 Lectures).
Summary (1 Lecture).
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
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- Assessment must maintain academic standards.
Assessment task Task type Weighting Learning outcomes Assignments Formative and summative 30% All Exam Summative 70% All
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course.
Assessment DetailThere will be four assignments worth 30% of the total mark. The remaining 70% will come from the exam
SubmissionAssignments must be handed in person to the lecturer or submitted in the assigned assignment box if they are to be marked.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
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